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Here's a plot of the complex roots of the equation $\Gamma(z+1) = 5^z$ near the origin.

Numerically it appears that the only other roots are those continuing along the three "rays" of roots pictured: the ray along the negative real axis (here the roots are near-integers) and the two symmetric arms which appear to tend to $\pi/3$ and $-\pi/3$ radians.